I have not been on a ship in Dec.--but there is a group of us that go every Jan. and we have no problem with rough waters. We sail in the Caribbean. I was told if you sail on a ship that is at least 70 gross tonage you won't feel anything because there are stabalizers that balance everything out. My husband gets sea sick on small boats and he has never had a problem on any of our cruises. There are medications you can take to help with sea sickness. Some of the people in our group take Bonine. You take it a few days before the cruise, every day while you're on the cruise and a few days after you get home. None of them have had any problems while using this medication. It's sold over the counter in Pharmacies. Good luck!!
As for the hidden cost for kids, I'm not much help there. I travel with a group that's all adults. I'm sure there will be some extra costs, but it's worth it just to be on a cruise. Most ships charge for sodas, but you can buy a soda card at the begining of the cruise and you will get unlimited soda. All the other drinks like milk, juice, tea, coffee and lemonaid are in the cost of the cruise. Of course alcohol is extra. There are kids programs on board, but I'm not sure about the cost. They also provide child care for a fee. Most of the main cruise stuff is in the cost of the cruise.
Hope this has been helpful, have a great cruise!